cp's OEIS Frontend

A264264 The length of the shortest nontrivial integral cevian of an isosceles triangle, with base of length 1 and legs of length n, that divides the base into two integral parts.

%I A264264 #10 Dec 10 2016 19:40:12
%S A264264 4,9,6,9,36,11,14,81,16,19,30,15,24,225,26,19,48,31,34,441,36,39,84,
%T A264264 35,44,69,32,49,900,51,34,87,56,59,1296,61,40,141,66,69,108,49,74,159,
%U A264264 64,53,126,81,84,2601,86,89,2916,91,94,147,66,61,66,101,70,165
%N A264264 The length of the shortest nontrivial integral cevian of an isosceles triangle, with base of length 1 and legs of length n, that divides the base into two integral parts.
%C A264264 A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).
%C A264264 A nontrivial cevian is one that does not coincide with a side of the triangle.
%C A264264 For all n, the longest nontrivial integral cevian has length n^2.
%H A264264 Colin Barker, <a href="/A264264/b264264.txt">Table of n, a(n) for n = 2..1000</a>
%H A264264 Wikipedia, <a href="http://en.wikipedia.org/wiki/Cevian">Cevian</a>
%H A264264 Wikipedia, <a href="http://en.wikipedia.org/wiki/Isosceles_triangle">Isosceles triangle</a>
%e A264264 a(4) = 6 because for legs of length 4 there are two cevians, of length 6 and 16, that divide the base into two integral parts.
%o A264264 (PARI)
%o A264264 ceviso(n) = {
%o A264264   my(d, L=List());
%o A264264   for(k=1, n^2,
%o A264264     if(issquare(n^2+k^2-k, &d) && d!=n,
%o A264264       listput(L, d)
%o A264264     )
%o A264264   );
%o A264264   Vec(L)
%o A264264 }
%o A264264 vector(100, n, n++; ceviso(n)[1])
%Y A264264 Cf. A264263.
%K A264264 nonn,easy
%O A264264 2,1
%A A264264 _Colin Barker_, Nov 10 2015